# Negating Quantified statements

The problem I am working on is:

Express each of these statements using quantifiers. Then form the negation of the statement, so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase “It is not the case that.”)

a) Some old dogs can learn new tricks. b)No rabbit knows calculus.

c) Every bird can fly.

d)There is no dog that can talk.

e) There is no one in this class who knows French and Russian.

## -------------------------------------------------------------------------------------------

I am having trouble with only two parts--namely, d) and e)

For d): P(x)= x cannot talk

$\exists xP(x)$ Negating this, $\neg \exists xP(x) \rightarrow \forall x \neg P(x)$

## Problem E

This is similar. Let me know if you need help with this one, and I'll edit my answer to include it.

-